Question

x3+y3+z3-3xyz=(x+y+z)(x2+y2+z2-xy-yz-zx) proof it LHS to RHS

Answer 1

So, we will work with the RHS part here,

(x + y+ z)( x² +y² +z² - xy - yz - zx)

Expanding the entire bracket,

= x³ + xy² + xz² - x²y - xyz -zx² + yx + y³ + yz² - xy² - y²z - xyz + zx² + zy² + z³ - xyz - yz² - z²x

=x³ + y³ +z³ - 3xyz

This is equal to LHS

Hence proved

Answer 2

x3+y3+z3-3xyz=(x+y+z)(x2+y2+z2-xy-yz-zx) proof it LHS to RHS

Solution = LHS = RHS

(Please check the attachment file)